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Regularity of the Parameter-to-State Map of a Parabolic Partial Differential Equation

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Extraction of Quantifiable Information from Complex Systems

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 102))

Abstract

In this paper, we present results that have been obtained in the DFG-SPP project “Adaptive Wavelet Frame Methods for Operator Equations: Sparse Grids, Vector-Valued Spaces and Applications to Nonlinear Inverse Problems”. This project has been concerned with (nonlinear) elliptic and parabolic operator equations on nontrivial domains as well as with related inverse parameter identification problems. In this paper we study analytic properties of the underlying parameter-to-state map, which is motivated by a parabolic model for the embryonal development of drosophila melanogaster.

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Author information

Authors and Affiliations

  1. DLR Oberpfaffenhofen, EOC, Münchner Str. 20, 82234, Wessling, Germany

    Rudolf Ressel

  2. University of Bremen, Zentrum für Technomathematik, Bibliothekstr. 1, 28359, Bremen, Germany

    Patrick Dülk & Peter Maass

  3. Philipps-University of Marburg, Hans Meerwein Str., Lahnberge, 35032, Marburg, Germany

    Stephan Dahlke

  4. University of Graz, Heinrichstr. 36, 8010, Graz, Austria

    Kamil S. Kazimierski

Authors
  1. Rudolf Ressel
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  2. Patrick Dülk
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  3. Stephan Dahlke
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  4. Kamil S. Kazimierski
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  5. Peter Maass
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Corresponding author

Correspondence to Rudolf Ressel .

Editor information

Editors and Affiliations

  1. FB 12 Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Stephan Dahlke

  2. Inst. Geometrie & Praktische Mathemathik, RWTH Aachen University, Aachen, Germany

    Wolfgang Dahmen

  3. Universität Bonn Institut für Numerische Simulation, Bonn, Germany

    Michael Griebel

  4. Max-Planck-Inst. f. Mathem. in d. Naturwissenschaften, Leipzig, Sachsen, Germany

    Wolfgang Hackbusch

  5. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Klaus Ritter

  6. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Reinhold Schneider

  7. Seminar für Angewandte Mathematik, ETH Zürich, Zürich, Switzerland

    Christoph Schwab

  8. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Harry Yserentant

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Ressel, R., Dülk, P., Dahlke, S., Kazimierski, K.S., Maass, P. (2014). Regularity of the Parameter-to-State Map of a Parabolic Partial Differential Equation. In: Dahlke, S., et al. Extraction of Quantifiable Information from Complex Systems. Lecture Notes in Computational Science and Engineering, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-08159-5_3

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